GATE 2024 ME – Question 52
The Levai type-A train illustrated in the figure has gears with module $m = 8$ mm/tooth. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates at 20 rev/min counter-clockwise. The magnitude of angular velocity of the arm is __________ rev/min. (*rounded off to 2 decimal places*)
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Correct answer: 15.50 to 15.66
Explanation
For an internal gear to mesh with the planet, which itself meshes with the central gear 2, the pitch radii add up: $r_4 = r_2 + 2r_3$, so $N_4 = 19 + 2(24) = 67$ teeth. With gear 2 fixed, the speeds relative to the arm give $\frac{\omega_4 - \omega_a}{0 - \omega_a} = -\frac{N_2}{N_4}$, so $\omega_4 - \omega_a = \frac{19}{67}\omega_a$ and $\omega_a = \omega_4\frac{67}{86} = 20 \times \frac{67}{86} = 15.58$ rev/min.